Method and apparatus for measuring thermal and electrical properties of thermoelectric materials

ABSTRACT

A method and apparatus for measuring and characterizing microscopic thermoelectric material samples using scanning microscopes. The method relies on concurrent thermal and electrical measurements using scanning thermal probes, and extends the applicability of scanning thermal microscopes (SThMs) to the characterization of thermoelectric materials. The probe makes use of two thermocouples to measure voltages at the tip and base of a cone tip of the probe. From these voltages, and from a voltage measured across the sample material, the Seebeck coefficient, thermal conductivity and resistance of the sample material can be accurately determined.

RELATED APPLICATIONS

The present application is related to commonly assigned and co-pendingU.S. patent application Ser. No. 09/641,871 entitled “Probe Apparatusand Method for Measuring Thermoelectric Properties of Materials,” whichis hereby incorporated by reference.

BACKGROUND OF THE INVENTION

1. Technical Field

The present invention is directed to a method and apparatus formeasuring thermal and electrical properties of thermoelectric materials.

2. Description of Related Art

One of the major difficulties in developing novel thin filmthermoelectric materials lies in obtaining consistent and accuratemeasurement of their thermal and electrical properties. Traditionalmethods cannot be easily extended to microscopic characterizationbecause of increased electrical and thermal parasitic losses associatedwith the probes used to perform the measurements. Additionally, the poorstructural stability of some of the novel materials being investigatedmakes using traditional probe methods unworkable.

For example, in the case of measurements using a probe, such as the“ZT-meter,” the time-scales of the transients become short and introduceerrors in electrical measurements. Thus it would be beneficial to havean apparatus and method capable of performing measurements of thermaland electrical properties of thermoelectric materials in which theproblems of the known methods with regard to thermal parasitic lossesand structural stability of the thermoelectric materials, is overcome.

SUMMARY OF THE INVENTION

The present invention provides a method and apparatus for measuring andcharacterizing microscopic thermoelectric material samples usingscanning atomic force microscopes. The methods rely on concurrentthermal and electrical measurements using scanning thermal probes, andextends the applicability of scanning thermal microscopes (SThMs) to thecharacterization of thermoelectric materials.

The probe of the present invention makes use of two temperature sensors,such as two thermocouples, to measure voltages at the tip and base of acone tip of the probe. From these voltages, and from a voltage measuredacross the sample material, the Seebeck coefficient, thermalconductivity and resistance of the sample material can be accuratelydetermined.

These thermoelectric properties may then be used in many differentapplications. For example, the thermoelectric properties may be used forcharacterization of scaled silicon devices wherein accurate spatialvariation of Seebeck coefficient yields an exact dopant profiling withthe silicon devices. Other features and advantages of the presentinvention will be described in or will become apparent to those ofordinary skill in the art in view of the following description of thepreferred embodiment.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features believed characteristic of the invention are setforth in the appended claims. The invention itself, however, as well asa preferred mode of use, further objectives and advantages thereof, willbest be understood by reference to the following detailed description ofan illustrative embodiment when read in conjunction with theaccompanying drawings, wherein:

FIG. 1 is an exemplary diagram illustrating a probe in accordance withthe present invention;

FIG. 2 is an exemplary cross-sectional view of the probe in accordancewith the present invention;

FIG. 3 is an exemplary circuit diagram illustrating the thermocouples ofthe probe;

FIG. 4 is an exemplary diagram illustrating the quantities used toperform temperature and heat flow calibration in accordance with thepresent invention;

FIGS. 5 and 6 are diagrams illustrating two methods of performing thecalibration in accordance with the present invention;

FIG. 7 is an exemplary graph of voltage versus temperature at the tip ofthe probe, the relationship having been obtained from temperaturecalibration of the probe;

FIG. 8 is an exemplary graph of Θ versus temperature differential, therelationship having been obtained from heat flow calibration of theprobe tip; and

FIG. 9 is an exemplary graph of Θ versus current for a material undertest.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention provides a method and apparatus for measuring andcharacterizing the thermal and electrical properties of thermoelectricmaterials. The invention makes use of temperature sensors, such asthermocouple and thermistor probe style temperature sensors, designatedfor thermal probes and uses a surface electrode at the thermal probe tipfor electrical measurements on a sample of the thermoelectric material.

The preferred embodiment of the present invention makes use of twothermocouples as the temperature sensors of the present invention.However, it should be appreciated that the present invention may useother types of temperatures sensors to measure the temperature values atvarious points on the probe without departing from the spirit and scopeof the present invention. For example, rather than two thermocouples,the present invention may use one or more thermistors in place of or inaddition to one or more of the thermocouples of the preferredembodiment. For purposes of illustration, however, the present inventionwill be described in terms of a probe having two therocouples which areused to measure temperature.

PROBE DESIGN

FIG. 1 is an exemplary diagram illustrating two views of a probe 100 inaccordance with the present invention. The probe shown in FIG. 1 is usedto measure the thermoelectric properties of thermoelectric materials ina manner described in detail hereafter. The probe in FIG. 1 makes use oftwo thermocouples to provide measurements of temperature that are thenused to calculate thermoelectric properties of the thermoelectricmaterial sample under test.

As shown in FIG. 1, the probe 100 includes a cantilever substratestructure 110, a first lead 120, a second lead 130, a third lead 140, afourth lead 145, a reflector 150, and a cone 160. The leads 120-145create two thermocouples which are used, in a manner to be describedhereafter, to measure the temperature of the probe tip (cone 160 tip)and the temperature of a sample material. From these measurements, thethermoelectrical properties of the sample material may be determined.

The reflector 150 is used to reflect a laser beam toward a detector (notshown). The laser beam, reflector 150 and detector are used to measurethe deflection of the cantilever structure 110 in order to maintain thedistance between the probe tip 160 and the sample material at a constantvalue.

FIG. 2 is an exemplary cross section of the probe tip 160. As shown inFIG. 2, the probe tip 160 is comprised of a number of different layersof material. The particular materials described hereafter with referenceto the exemplary embodiment are meant to be for illustrative purposesand other materials having similar properties may be used in replacementor in addition to the materials described herein without departing fromthe spirit and scope of the present invention.

The formation of the probe tip 160 will now be described with referenceto FIG. 2. The mechanisms used to create the various layers of theprobe, such as deposition and etching, are generally known in the art ofsemiconductor chip manufacture. However, these mechanisms have notpreviously been used to create the structure herein described.

The cantilever substrate 110 is created first and is comprised of asilicon or silicon nitride material. A silicon oxide cone 160 is formedon the cantilever substrate 110. A secondary metal layer is then createdover the substrate 110 and the cone 160. The secondary metal layer maybe, for example, chromium, and is used to create the second lead 130 andthird lead 140.

It should be noted that the chromium layer does not cover all of thesurface of the substrate 110 and cone 160. Rather, as shown in FIG. 2, aportion of the chromium layer at the base of the cone is etched away sothat the two leads 130 and 140 are formed without touching one another.

Once the two leads 130 and 140 are created, a silicon oxide layer 180 iscreated on top of the chromium layer. The silicon oxide layer 180 isetched at the apex of the cone and at a point at the base of the cone tocreate two thermocouples which will be used in the present invention toperform thermoelectric property measurements of sample materials.

After the silicon oxide layer 180 is created, the primary metal layer120 is created. The primary metal layer 120 is comprised ofplatinum/iridium in an exemplary embodiment, but may be any other typeof metal which may be determined to have properties especially wellsuited for a particular application. As shown in FIG. 2, the primarymetal layer 120 is etched away at position near the base of the cone tothereby create the first and fourth leads 120 and 145.

The interaction of the primary and secondary metal layers at the pointswhere the silicon oxide layer 180 was etched away, creates thethermocouples which are used for measurements of thermoelectricproperties. Additional layers of material may be added to the structureshown in FIG. 2 so long as these additional layers do not interfere withthe operation of the dual thermocouples. For example, fine wires may beadded to the cantilever structure 110 for heating the cantileverstructure to thereby create a temperature differential, as will bedescribed hereafter.

While the probe structure shown in FIGS. 1 and 2 show a cone-shapedprobe tip, the probe tip may be of any shape desirable. For example, thecone-shaped probe tip may be vary narrow or very wide in diameter, mayhave any value interior angle at the tip, and the like. However, anarrower tip is preferable since the tip localizes measured temperaturefields to a smaller area and thus, makes the probe capable of measuringthermoelectric properties of smaller scale materials.

The probe created using the process described above can be used formaking measurements in many different applications. The probe may beused to measure thermoelectric properties of nano-scale structures,profiling of silicon dopants of semiconductor materials, characterizinggiant magneto-resistive heads, and the like. The present invention isnot limited to any one application of the probe and is intended to coverall possible applications to which the probe may be made.

Those of ordinary skill in the art will appreciate that the probe of thepresent invention is utilized along with a computing system in which thecalibration and computations described hereafter are performed. Theprobe is used to provide measured quantities which are then processed bythe computing system to calibrate the probe and generate values for thethermoelectric properties of the materials under test.

Calibration of the Probe

Before the probe can be used to measure the thermoelectric properties ofsample materials, the probe must be calibrated. The calibration isperformed using a sample whose thermoelectric properties are generallyknown in order to obtain a relationship of thermoelectric properties.The calibration method generally includes the steps of:

1) measuring the voltages across each of the thermocouples;

2) measuring the temperature from a bottom lead to the back side of thesample;

3) calibrating temperature according to NIST standards based on theabove measurements; and

4) calibrating heat flow using the known thermoelectrical properties ofthe sample.

FIG. 3 shows a circuit schematic for a mixed mode operation probe inaccordance with the present invention. As shown in FIG. 3, the probe 100consists of a first lead 120, a second lead 130, and a third lead 140.The voltage V_(t1) across the first and second leads 120 and 130,connected to the thermocouple at the tip 160, are used to monitor thetemperature and the heat flow out of the tip of the cone of the probe.The voltage V_(t2) across the third and fourth leads 140 and 145,connected to the thermocouple at the base, are used to monitor thetemperature and the heat flow at the base of the cone of the probe.Based on these voltages, the difference in temperature ΔT_(t) betweenthe tip and base of the cone can be calculated. Current-voltage (I-Vs)measurements at the first and fifth leads 120 and 330 characterize theelectrical properties of the thermoelectric material sample 310.

The temperature sensors, i.e. thermocouples, at the tip may becalibrated in a number of different ways. In particular, the preferredembodiment of the present invention calibrates the temperature sensorsat the tip by scanning the probe tip over a base of a pre-calibratedsurface and over a metal surface of a thermoelectric cooler 320concurrently. For example, the pre-calibrated material may be a platinumbase of a pre-calibrated silicon diode mounted on the thermoelectriccooler and the metal surface may be a copper metal surface of thethermoelectric cooler 320, as shown in FIG. 5. In separate calibration,scanning a metal surface of a thermoelectric cooler may be concurrentlymonitored by a pre-calibrated E-type thermocouple, for example, as shownin FIG. 6. Regardless of the particular manner by which calibration isperformed, the method of temperature calibration is essentially thesame.

The temperature sensors, i.e. thermocouples, at the tip and base of thecone 160 are used to measure voltage values for various tip and sampletemperatures. With the present invention, a laser, which may be used maybe used to detect cantilever deflection of the probe 100, is switchedOFF and the thermoelectric cooler 320 is activated to increase anddecrease the temperature of the sample near the ambient.

Measurements of the voltages V_(t1) and V_(t2) are made using thethermocouples and are used to plot a relationship between the voltagesand the temperature of the precalibrated surface. Using NationalInstitute of Standards and Technology (NIST) temperature standards, arelationship of voltage to temperature is identified using known points.FIG. 7 shows an exemplary relationship between the tip voltage and thetip temperature. In this way, a one-to-one relation table between thethermocouple sensor voltage V and the temperature T may be obtained.

Although the above method is used in the preferred embodiment of thepresent invention, other methods of performing temperature calibrationmay be used with the present invention without departing from the spiritand scope of the present invention.

Once temperature calibration is performed, the thermocouple sensors mustbe calibrated for measurement of heat flow. The heat flow calibrationmakes use of a material having known thermoelectric properties. Inparticular, materials having known Seebeck coefficient α and thermalconductivity λ_(k), are utilized.

FIG. 4 is an exemplary diagram that illustrates the basic method of heatcalibration in accordance with the present invention. The heat flow Qfrom the tip to the sample surface is calibrated by scanning the probetip in a contact-mode of operation over thermoelectric materials, suchas Bi_(0.5)Sb_(1.5)Te₃, Bi₂Te_(2.9)Se_(0.1), ZnSb, and Bi crystals,whose Seebeck coefficient α_(known) and thermal conductivity λ_(known)are known. The heat flow balance results in the following equation:

Q _(p)(ΔT _(t))=Gλ _(k) ΔT _(s)  (1)

where ΔT_(s) is the temperature drop across the sample and G is ageometric parameter. G≈2πα where α is the “thermal” radius of the probetip. The value for ΔT_(s) equals the ratio of the voltage across thethermocouple between leads 120 and 140 and the Seebeck coefficient ofthe material (V/α). The open circuit voltage V_(known) is measuredacross leads 120 and 330. Thus, the equation becomes: $\begin{matrix}{\frac{Q_{p}\left( {\Delta \quad T_{t}} \right)}{G} = {\lambda_{known}\left( {V_{known}/\alpha_{known}} \right)}} & (2)\end{matrix}$

As shown in FIG. 8, the quantity (Q_(p)/G), denoted by Θ, which issometimes referred to as the normalized heat flow, can be tabulated forstandard conditions, e.g., when the laser used for monitoring deflectionis turned OFF (curve a) and turned ON (curve b). Θ=0 at T_(t)=0 when thelaser is OFF, and at T_(t)=ΔT₁ when the laser is ON. Thus, from thetemperature and heat flow calibrations above, the relationshipsV_(t)/T_(t) and Θ/ΔT_(t) provide a complete thermoelectric calibrationand characterization of the probe tip.

Thermoelectric Characterization of Materials

After calibration, the present invention may be used to thermallycharacterize thermoelectric materials. The method and apparatus of thepresent invention exploit the open-circuit condition: I=0. With themethod and apparatus of the present invention, the tip voltage V_(t) andopen-circuit voltage V_(so) are concurrently measured over thethermoelectric sample of unknown thermal conductivity λ and Seebeckcoefficient a with a calibrated probe tip. T_(b), the backsidetemperature of the sample, is varied by cooling the backside of thesample above and below the ambient. Alternatively, if there are heaterwires provided in the cantilever structure 110, the tip may be heated bypassing high current through the heater wires. Any method of creating atemperature difference across the sample may be used without departingfrom the spirit and scope of the present invention. In doing so, thefollowing relationship is obtained: $\begin{matrix}{{\lambda \quad \Delta \quad T_{s}} = {\frac{\lambda \quad V_{s}}{\alpha} = {\Theta \left( {\Delta \quad T_{t}} \right)}}} & (3)\end{matrix}$

where λ is an unknown thermal conductivity of the material and a is anunknown Seebeck coefficient of the material.

The ratio of the thermal conductivity of the material to its Seebeckcoefficient can be measured precisely from equation (3), independent ofthe interface properties between the probe tip and the sample:$\begin{matrix}{\frac{\lambda}{\alpha} = \frac{\Theta \left( {\Delta \quad T_{t}} \right)}{V_{s}}} & (4)\end{matrix}$

If either the thermal conductivity or the Seebeck coefficient is known,the other parameter can be accurately determined using the relationshipabove. This is especially useful, for example, when performing dopantprofiling of silicon wafer chips. Since the thermal conductivity ofsilicon is a known value, measurements of the Seebeck coefficient byscanning the probe of the present invention across the chip, can be usedto obtain an accurate profile of the dopants in the chip structure. Inaddition, these values can also be used to calculate the coolingcapacity of thermoelectric coolers.

Electrical Characterization of Materials

The electrical characterization exploits the thermal isolationcondition: Q_(p)=0 or Θ=0. Under this condition, there is no temperaturedrop across the interface between the tip and the thermal sensor. Thetip thermal sensor measures the temperature of the sample. An electriccurrent is passed through the tip to attain this condition.

In the above example, the backside of the sample is maintained attemperature greater than the ambient temperature (T_(b)>T_(a)) so thatΘ=λΔT_(s)<0 at I=0. The electric current I produces cooling at thecontacts and results in the condition Θ=0 and T_(t)=T_(s) at I=I₁. Ifthe current is increased further, the cooling effect increases and Θattains a maximum when the surface temperature is such that the Jouleheating balances the thermoelectric cooling effects. Further increase inI results in lower Θ and another Θ=0 condition at I=I₂. Thethermoelectric voltage (αΔT_(s)) is the same at I=I₁ and I=I₂:$\begin{matrix}{{R + R_{c}} = {\frac{\left( {V_{s2} - V_{s1}} \right)}{\left( {I_{2} - I_{1}} \right)}\quad {and}}} & (5) \\{\alpha = \frac{\left( {{I_{2}V_{s1}} - {I_{1}V_{s2}}} \right)}{\left( {I_{2} - I_{1}} \right)\left( {T_{b} - T_{t}} \right)}} & (6)\end{matrix}$

where R is the resistance of the sample material and R_(c) is theelectrical contact resistance of the contact between the probe and thesample material.

Alternatively (especially if the magnitude of the current I needs to belimited to small values for ultrathin films of the order of 100 nms),the Θ=0 can be obtained for two different values of T_(b) by changingthe current of the external thermoelectric cooler. If the correspondingvalues of I are I₀₁ and I₀₂, the I-V relations for the two cases are:

V _(s1) =I ₀₁(R+R _(c))+α(T _(t) −T _(b1))

V _(s2) =I ₀₂(R+R _(c))+α(T _(t) −T _(b2))  (7)

Solving the simultaneous equations results in: $\begin{matrix}{{R + R_{c}} = {\frac{\left\lbrack {{\left( {T_{t} - T_{b1}} \right)V_{s2}} - {\left( {T_{t} - T_{b2}} \right)V_{s1}}} \right\rbrack}{\left\lbrack {{\left( {T_{t} - T_{b1}} \right)I_{o2}} - {\left( {T_{t} - T_{b2}} \right)I_{o1}}} \right\rbrack}\quad {and}}} & (8) \\{\alpha = \frac{\left( {{I_{o2}V_{s1}} - {I_{o1}V_{s2}}} \right)}{\left\lbrack {{\left( {T_{t} - T_{b1}} \right)I_{o2}} - {\left( {T_{t} - T_{b2}} \right)I_{o1}}} \right\rbrack}} & (9)\end{matrix}$

Once the Seebeck coefficient α is known, the thermal conductivity λ canbe calculated using the equation (4). Moreover, the Seebeck coefficientand the resistivity of the sample material can be calculated using theabove relationships and the following relationships relating to thermalconductance. With these thermoelectric properties of the samplematerial, the cooling performance of the sample material can beaccurately determined.

Thermal Conductance

Although the thermal conductivity λ can be calculated independent of thethermal conductance of the element, it is important to extract thethermal conductance of the thermoelectric element for estimating thecontact resistances. In order to extract the thermal conductance, letthe temperature differential across the sample material be ΔT_(s) andthe corresponding open-circuit voltage be V_(so)=αΔT_(s). One method toobtain the thermal conductance is to measure the differential change inelectrical and thermal characteristics when the sample material isperturbed with a small current i about I=0. The heat balance conditionsat the tip-sample surface for small positive-and negative-currents ofmagnitude i will be:

Cooling Mode:

Q(T _(t) +δT _(t))=αi(T _(b) +ΔT _(s) −δT _(s))−xi ² R−i ² R _(c) +K(ΔT_(s) −δT _(s))  (10)

Heating Mode:

 Q(T _(t) +δT _(t))=−αi(T _(b) +ΔT _(s) +δT _(s))−xi ² R−i ² R _(c)+K(ΔT _(s) +δT _(s))  (11)

where δT_(t) and δT_(s) are the perturbations in tip temperature andsample surface temperature and x denotes the fraction of Joule heatgenerated in the thermoelement that flows back to the tip.

If Q(T_(t)+δT_(t))−Q(T_(t)−δT_(t))=2δQ, the following relation can beobtained based on equations (10) and (11): $\begin{matrix}{{\delta \quad T_{s}} = \frac{{\alpha \quad {i\left( {T_{b} + {\Delta \quad T_{s}}} \right)}} - {\delta \quad Q}}{K}} & (12)\end{matrix}$

The voltages across the thermoelement for positive and negative valuesof current are:

V _(s) +δV=i(R+R _(c))+α(ΔT _(s) −δT _(s))

V _(s) −δV=i(R+R _(c))+α(ΔT _(s) +δT _(s))  (13)

Hence, the differential voltage about the zero-current bias point can begiven by:

ΔT _(s) =i(R+R _(c))−αδT _(s)  (14)

Substituting the value of δT_(s) from equation (12) and noting thatδQ/K=δΘ/λ results in a thermal resistance: $\begin{matrix}{K = \frac{\alpha^{2}{i\left( {T_{b} + {\Delta \quad T_{s}}} \right)}}{\left\lbrack {{i\left( {R + R_{c}} \right)} - {\delta \quad V} - {\left( \frac{\alpha}{\lambda} \right)\delta \quad \Theta}} \right\rbrack}} & (15)\end{matrix}$

Note that the relation is valid even for the particular case of ΔT_(s)=0and T_(b)=T_(a). The conductance can thus be accurately estimated bymeasuring the amplitude of the variations of δV and δΘ for asinusoidal/bipolar step variation of I.

Estimation of Contact Impedances

In the thermal characterization dealing with the open-circuit conditionI=0, the heat flow through the tip to the sample surface is equal to theheat flow into the sample. This condition can be used to estimate thecontact thermal resistance K_(c).

Q=K _(c)(T _(t) −T _(s))=K(T _(s) −T _(b))  (16)

or,$K_{c} = {{K\left( \frac{\Delta \quad T_{s}}{T_{t} - T_{b} - {\Delta \quad T_{s}}} \right)} = {K\left( \frac{V_{so}/\alpha}{T_{t} - T_{b} - {V_{so}/\alpha}} \right)}}$

Hence, $\begin{matrix}{K_{c} = {K\left\lbrack \frac{V_{so}}{\alpha\left( {T_{t} - T_{b)} - V_{so}} \right.} \right\rbrack}} & (17)\end{matrix}$

The electrical contact resistance R_(c) can be estimated by modeling theproperties of the interface between the cone tip and the samplematerial. If it is assumed that the contact resistances are primarilyelectronic in nature and are related by a boundary form of theWiedmann-Franzlaw, the following relation is obtain: $\begin{matrix}{R_{c} = \frac{L_{0}T_{s}}{K_{c}}} & (18)\end{matrix}$

where L₀˜(156μV/K)² is the Lorentz number. Equations (5) and (8) canyield a value for the intrinsic thermoelement resistance if the contactresistance R_(c) is known.

It is important to note that while the present invention has beendescribed in the context of a probe apparatus coupled to a fullyfunctioning data processing system, those of ordinary skill in the artwill appreciate that the processes of the present invention are capableof being distributed in the form of a computer readable medium ofinstructions and a variety of forms and that the present inventionapplies equally regardless of the particular type of signal bearingmedia actually used to carry out the distribution. Examples of computerreadable media include recordable-type media, such as a floppy disk, ahard disk drive, a RAM, CD-ROMs, DVD-ROMs, and transmission-type media,such as digital and analog communications links, wired or wirelesscommunications links using transmission forms, such as, for example,radio frequency and light wave transmissions. The computer readablemedia may take the form of coded formats that are decoded for actual usein a particular data processing system.

The description of the present invention has been presented for purposesof illustration and description, and is not intended to be exhaustive orlimited to the invention in the form disclosed. Many modifications andvariations will be apparent to those of ordinary skill in the art. Theembodiment was chosen and described in order to best explain theprinciples of the invention, the practical application, and to enableothers of ordinary skill in the art to understand the invention forvarious embodiments with various modifications as are suited to theparticular use contemplated.

What is claimed is:
 1. A method of measuring thermoelectriccharacteristics of a material, comprising: creating a temperaturedifference across the material; measuring, with a probe, a voltageacross the material; measuring a difference in temperature between a tipof the probe and a base of the probe; and calculating at least onethermoelectric characteristic based on the measured temperaturedifference and the measured voltage across the material.
 2. The methodof claim 1, wherein creating a temperature difference across thematerial includes using a thermoelectric cooler at a base of thematerial to cool the material.
 3. The method of claim 1, whereincreating a temperature difference across the material includes passing ahigh current through a heater wire associated with the probe.
 4. Themethod of claim 1, wherein measuring a voltage across the materialincludes passing a current through a circuit comprising a lead to thetip of the probe and a lead to a base of the material.
 5. The method ofclaim 1, wherein measuring a difference in temperature between the tipof the probe and the base of the probe includes measuring a firstvoltage across a first thermocouple associated with the tip of the probeand measuring a second voltage across a second thermocouple associatedwith the base of the probe.
 6. The method of claim 5, wherein thedifference in temperature is calculated based on a relationship ofvoltage at the tip to temperature at the tip and a relationship of heatflow across the probe to the difference in temperature across the probe.7. The method of claim 1, wherein calculating at least onethermoelectric characteristic includes determining a relationship ofthermal conductivity to Seebeck coefficient.
 8. The method of claim 7,wherein the relationship of thermal conductivity to Seebeck coefficientis a ratio of a normalized heat flow, as a function of a voltage at thetip of the probe, to a voltage across the material.
 9. The method ofclaim 1, wherein calculating at least one thermoelectric characteristicincludes determining a relationship of resistance of the material and arelationship of Seebeck coefficient of the material based on a voltageacross the material, a current across the material, a temperature at thetip of the probe and a temperature at a back of the material for acondition where a normalized heat flow is zero.
 10. The method of claim9, wherein the relationship of resistance of the material is:${R + R_{c}} = \frac{\left\lbrack {{\left( {T_{t} - T_{b1}} \right)V_{s2}} - {\left( {T_{t} - T_{b2}} \right)V_{s1}}} \right\rbrack}{\left\lbrack {{\left( {T_{t} - T_{b1}} \right)I_{o2}} - {\left( {T_{t} - T_{b2}} \right)I_{o1}}} \right\rbrack}$

where R is an electrical resistance of the material, R_(c) is anelectrical resistance of an electrical contact between the tip of theprobe and the material, I_(o1) is a current at a first coolingtemperature T_(b1) where the normalize heat flow is zero, V_(s1) is avoltage across the material at the first cooling temperature, I_(o2) isa current at a second cooling temperature T_(b2) where the normalizedheat flow is zero, V_(s2) is a voltage across the material at the secondcooling temperature, and T_(t) is the temperature at the tip of theprobe.
 11. The method of claim 9, wherein the relationship of Seebeckcoefficient is$\alpha = \frac{\left( {{I_{o2}V_{s1}} - {I_{o1}V_{s2}}} \right)}{\left\lbrack {{\left( {T_{t} - T_{b1}} \right)I_{o2}} - {\left( {T_{t} - T_{b2}} \right)I_{o1}}} \right\rbrack}$

where I_(o1) is a current at a first cooling temperature T_(b1) wherethe normalize heat flow is zero, V_(s1) is a voltage across the materialat the first cooling temperature, I_(o2) is a current at a secondcooling temperature T_(b2) where the normalized heat flow is zero,V_(s2) is a voltage across the material at the second coolingtemperature, and T_(t) is the temperature at the tip of the probe. 12.The method of claim 1, wherein calculating at least one thermoelectriccharacteristic includes calculating a thermal resistance of the materialbased on a Seebeck coefficient of the material, a temperature dropacross the material, a temperature of a back side of the material, aperturbation current, an electrical resistance of the material, anelectrical resistance of a contact between the tip of the probe and thematerial, and a thermal conductivity of the material.
 13. The method ofclaim 1, wherein calculating at least one thermoelectric characteristicincludes determining a thermal resistance of the material based on therelationship:$K = \frac{\alpha^{2}{i\left( {T_{b} + {\Delta \quad T_{s}}} \right)}}{\left\lbrack {{i\left( {R + R_{c}} \right)} - {\delta \quad V} - {\left( \frac{\alpha}{\lambda} \right)\delta \quad \Theta}} \right\rbrack}$

Where α is a Seebeck coefficient of the material, i is a small current,T_(b) is a temperature at a back of the material, ΔT_(s) is atemperature drop across the material, R is an electrical resistance ofthe material, R_(c) is an electrical resistance of a contact between thetip of the probe and the material, δV is a change in voltage, δΘ is achange in normalized heat flow, and λ is a thermal conductivity of thematerial.
 14. The method of claim 1, wherein calculating at least onethermoelectric characteristic includes determining an electricalresistance of a contact between the tip of the probe and the material asa function of the Lorentz number, temperature of the material and athermal resistance at the contact.
 15. The method of claim 1, whereincalculating at least one thermoelectric characteristic includesdetermining an electrical resistance of a contact between the tip of theprobe and the material using the relationship:$R_{c} = \frac{L_{0}T_{s}}{K_{c}}$

where L_(o) is the Lorentz number T_(s) is a temperature of thematerial, and K_(c) is thermal resistance at the contact.
 16. The methodof claim 1, wherein measuring a difference in temperature between thetip of the probe and the base of the probe includes measuring thetemperature at the tip of the probe using a first temperature sensor andmeasuring the temperature at the base of the probe using a secondtemperature sensor.
 17. The method of claim 16, wherein at least one ofthe first temperature sensor and the second temperature sensor is one ofa thermocouple and a thermistor.
 18. A computer program product in acomputer readable medium for measuring thermoelectric characteristics ofa material, comprising: first instructions for creating a temperaturedifference across the material; second instructions for measuring, witha probe, a voltage across the material; third instructions for measuringa difference in temperature between a tip of the probe and a base of theprobe; and fourth instructions for calculating at least onethermoelectric characteristic based on the measured temperaturedifference and the measured voltage across the material.
 19. Thecomputer program product of claim 18, wherein the first instructions forcreating a temperature difference across the material includeinstructions for using a thermoelectric cooler at a base of the materialto cool the material.
 20. The computer program product of claim 18,wherein the first instructions for creating a temperature differenceacross the material include instructions for passing a high currentthrough a heater wire associated with the probe.
 21. The computerprogram product of claim 18, wherein the second instructions formeasuring a voltage across the material include instructions for passinga current through a circuit comprising a lead to the tip of the probeand a lead to a base of the material.
 22. The computer program productof claim 18, wherein the third instructions for measuring a differencein temperature between the tip of the probe and the base of the probeinclude instructions for measuring a first voltage across a firstthermocouple associated with the tip of the probe and measuring a secondvoltage across a second thermocouple associated with the base of theprobe.
 23. The computer program product of claim 22, wherein thedifference in temperature is calculated based on a relationship ofvoltage at the tip to temperature at the tip and a relationship of heatflow across the probe to the difference in temperature across the probe.24. The computer program product of claim 18, wherein the fourthinstructions for calculating at least one thermoelectric characteristicinclude instructions for determining a relationship of thermalconductivity to Seebeck coefficient.
 25. The computer program product ofclaim 24, wherein the relationship of thermal conductivity to Seebeckcoefficient is a ratio of a normalized heat flow, as a function of avoltage at the tip of the probe, to a voltage across the material. 26.The computer program product of claim 18, wherein the fourthinstructions for calculating at least one thermoelectric characteristicinclude instructions for determining a relationship of resistance of thematerial and a relationship of Seebeck coefficient of the material basedon a voltage across the material, a current across the material, atemperature at the tip of the probe and a temperature at a back of thematerial for a condition where a normalized heat flow is zero.
 27. Thecomputer program product of claim 18, wherein the fourth instructionsfor calculating at least one thermoelectric characteristic includeinstructions for calculating a thermal resistance of the material basedon a Seebeck coefficient of the material, a temperature drop across thematerial, a temperature of a back side of the material, a perturbationcurrent, an electrical resistance of the material, an electricalresistance of a contact between the tip of the probe and the material,and a thermal conductivity of the material.
 28. The computer programproduct of claim 18, wherein the fourth instructions for calculating atleast one thermoelectric characteristic include instructions fordetermining an electrical resistance of a contact between the tip of theprobe and the material as a function of the Lorentz number, temperatureof the material and a thermal resistance at the contact.
 29. Anapparatus for measuring thermoelectric characteristics of a material,comprising: a means for creating a temperature difference across thematerial; and a probe for measuring a voltage across the material andfor measuring a difference in temperature between a tip of the probe anda base of the probe, wherein at least one thermoelectric characteristicis determined based on the measured temperature difference and themeasured voltage across the material.
 30. The apparatus of claim 29,further comprising a computer for determining the at least onethermoelectric characteristic.
 31. The apparatus of claim 30, whereinthe at least one thermoelectric characteristic is determined using arelationship of thermal conductivity to Seebeck coefficient.
 32. Theapparatus of claim 30, wherein the at least one thermoelectriccharacteristic is determined based on a relationship of resistance ofthe material and a relationship of Seebeck coefficient of the materialbased on a voltage across the material, a current across the material, atemperature at the tip of the probe and a temperature at a back of thematerial for a condition where a normalized heat flow is zero.
 33. Theapparatus of claim 29, wherein the probe includes a first temperaturesensor for measuring the temperature at the tip of the probe and asecond temperature sensor for measuring the temperature at the base ofthe probe.
 34. The apparatus of claim 33, wherein at least one of thefirst temperature sensor and the second temperature sensor is one of athermocouple and a thermistor.